Immutable in this context refers to an OS that can’t be changed while running. Steam deck does something like that. Basically the all of the OS system files are read only, so that the user or some malware can’t Bork the system. The only parts that are writable are the users profile directory and the logs.
You can still receive updates and install apps. It’s just that that’s handled a bit differently than with a standard OS.
E.g. it could be that the OS provider only issues complete updates, and then you either have to reboot. This is the case with steam os on the steam deck. The System portion of the OS is mounted read only during use.
If the immutability in OS is well designed, then there shouldn’t be really an downsides or loss in comfort. That is, unless you’re a linux expert and like to tinker under the hood.
The general idea is, the core of the OS if read-only, and everything else that needs to be modified is mounted writeable. Ideally, protecting the core of the OS from writes, should for example prevent malware from installing a modified kernel or boot loader. Or maybe preventing the user from accidentally borking something so that their system becomes unbootable. How much of an advantage that is practice is dependent on use case. In the case of Steam OS on the steam deck, it’s perfect, since boot issues on the steam deck could potentially be tricky to fix as opposed to a standard PC.
Another advantage of immutable could theoretically be wear and tear of certain storage devices. e.g. Think of a raspberry PI and SDcards. If you could have most of the important stuff of the OS as read only on the SD card, and everything else on a usb disk or even an NFS mount, then the SD card should last much longer since no writes are happening on it.
As far as true security benefit is concerned… I can’t really say. It depends on how updates and eventual writes are actually handled to the immutable part of the OS. Obviously at some point, changes do happen. Like during a system update. In the case of Steam OS, The system portion is wiped and replaced the new version. Chimera OS, did something similar (I don’t know if they still use the same method). They had a read-only BTRFS partition, where they would then provide a new snapshot during an update, which would be downloaded and applied at the next reboot. This approach would hinder automated crypto malware for example (at least for system files).